• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.6
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• pp.411-416
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• 2016

This paper presents the design methodology of an unknown input observer for Lipschitz nonlinear systems with unknown inputs in the framework of convex optimization. We use an unknown input observer (UIO) to consider both nonlinearity and disturbance. By deriving a sufficient condition for exponential stability in the linear matrix inequality (LMI) form, existence of a stabilizing observer gain matrix of UIO will be assured by checking whether the quadratic stability margin of the error dynamics is greater than the Lipschitz constant or not. If quadratic stability margin is less than a Lipschitz constant, the coordinate transformation may be used to reduce the Lipschitz constant in the new coordinates. Furthermore, to reduce the maximum singular value of the observer gain matrix elements, an object function to minimize it will be optimally designed by modifying its magnitude so that amplification of sensor measurement noise is minimized via multi-objective optimization algorithm. The performance of UIO is compared to a nonlinear observer (Luenberger-like) with an application to a flexible joint robot system considering a change of load and disturbance. Finally, it is validated via simulations that the estimated angular position and velocity provide true values even in the presence of unknown inputs.

• Geomechanics and Engineering
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• v.13 no.3
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• pp.517-533
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• 2017

In this paper, with a graphical approach, a series of stability charts for homogeneous slopes with benches are presented based on the upper bound limit analysis theory and strength reduction technique. The objective function of the slope safety factor $F_s$ is optimized by the nonlinear sequential quadratic programming, and a substantial number of examples are illustrated to use the stability charts for homogeneous slopes with benches driven by only the action of the soil weight. These charts can be applied to quick and accurate estimations of the stability status of homogeneous slopes with benches. Moreover, the failure modes and the formula for safety factor Fs of homogeneous slopes with benches are provided to illustrate the stability analysis of slopes with benches, which is validated by samples.

• Journal of Navigation and Port Research
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• v.36 no.5
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• pp.379-385
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• 2012

In this paper, the stability and stabilization problems for marine vessels including surface and underwater vehicles are described. In the marine vessels, there are many and strong nonlinear parameters. These give hard design process and difficulties to us. In this article, at first we make a descriptor system representation as a controlled system to preserve the physical parameters of the system as it is. And we propose a new stability and stabilizability conditions based on the quadratic stabilization approach which gives a solution for the unreasonable problems produced by added mass. That is, the proposed conditions are not interfered with the nonsymmetric matrix constraint. And the stability condition is given by an matrix inequality such that it makes us to obtain a solution easily for something.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.707-721
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• 2013

In this paper, we investigate a fuzzy version of stability theory for the following functional equation f(x+y)+f(x-y)-2f(x)-f(y)-f(-y)=0 in the sense of M. Mirmostafaee and M. S. Moslehian.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.203-208
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• 1987

Design problem of output feedback controllers for discrete large scale systems using simplified model is investigated. It is shown that neglecting fast modes does not generally guarantee the stability of the closed loop system. In this paper, the design procedure is proposed to stabilize the system by minimizing a quadratic cost function for the simplified model and a measure of stability for the neglected fast model.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2003.06a
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• pp.188-192
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• 2003

Pole placement method is widely used in controller design. For the stability of the closed loop system, user-specified desired locations including extra pole locations in the s-plane is chosen and by some procedure, feedback gain is obtained. In this paper, only desired pole location is used, and the calculation process is done for attaining linear quadratic stability. Similarly transformation is used for this. By computer simulations using MATLAB, the effectiveness is shown.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.779-787
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• 2019

In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.6
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• pp.641-646
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• 1999

This paper deals with the robust stability of discrete-time linear systems with time- varying delays and norm-bounded uncertainties. In this paper, the magnitude of time-varying delays is assumed to be upper-bounded. The sufficient condition is presented in terms of linear matrix inequality. It is also shown that the robust stability of uncertain discrete-time linear systems with time-varying delays is related with the quadratic stability of uncertain discrete-time linear systems with constant time delay.

• Journal of Industrial Technology
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• v.10
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• pp.3-8
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• 1990

This paper presents a linear state feedback control approach to the stabilization of discrete-time uncertain systems with bounded uncertain parameters. The approach is based on the LQ(linear quadratic) regulator theory and Lyapunov's stability analysis. Asymptotically stable behavior is guaranteed in the presence of parameter uncertainties, and the upper bound of the performance index is determined.